Hi

I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)?
Cross NumberArea sq cm
15
213
325
441
561

I also need to know what the formula is for it?

Please help me
Joel

Hi Joel,

I wish I could see a diagram I don't know where the numbers come from and what the cross looks like. I approached this with differences.

 5 13 25 41 61 8 12 16 20 4 4 4
In the rows after the first, each number is the difference of the 2 numbers in the row above it. 13 - 5 = 8, 25 - 13 = 12,... Since the third row is composed entirely of 4's I can see how to find a rule that will generate the terms.

If I have 3 consecutive terms in the first row

an-1, an, an+1

then the two numbers in the row directly below these 3 are

an - an-1, an+1 - an

Taking differences a second time, the number below these 2 in the third row is

(an+1 - an) - (an - an-1)

But all the numbers in the third row are 4 and henve

(an+1 - an) - (an - an-1) = 4

and hence
an+1 = 2 an - an-1 + 4

Thus if you know the first two terms are a1 = 5 and a2 = 13 you can generate the rest. For example

a3 = 2 a2 - a1 + 4 = 2 13 - 5 + 4 = 25

Cheers,
Penny

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